Evolution of meso-structures and mechanical properties of granular materials under triaxial compression state from complex network perspective

Abstract

The evolution of the network connection of granular materials is investigated by performing a series of numerical simulations in triaxial compression tests with different initial porosities by discrete element method (DEM). Results of evolution characteristics of complex network are reported for both dense and loose assembles. The simulation focuses on the influence of porosity on connectivity evolution, and reveals the correlation between the parameters in macro and mesoscale. Kinds of properties are studied, including degree and its distribution, clustering coefficient, network density and the average shortest path. The results demonstrate the phenomenon of dilataion due to shear deformation are able to be reflected by those mesocope parameters mentioned. Specifically, in the process of the dilatation, the rate of contact disintegration exceeds the rate of contact creation, which means the loss of connectivity, thus the values of some properties decrease, like degree, clustering coefficient and network density, but some increase like the average shortest path. Additionally, the bridging of macro and mesoscope are built regarding the parameters of the Cam-Clay model and complex network. From the results, the parameter M (determined by q = Mp′ at critical state) and the reference parameter $$ {\text{T}} $$ ( $$ T_{j}^{s} = L_{j}^{s} \left( {1 - \log_{{D_{j}^{s} }} t} \right) $$ , calculated according to the average degree $$ D_{j}^{s} $$ and shortest path $$ L_{j}^{s} $$ of the critical state) have a positive correlation. And a linear relationship between the slope of isotropic virgin-consolidation λ and the rate of decline of the average shortest path upon loading is represented as well. These achievements are the first step in an ongoing study of establishing the multi-scale constitutive from complex network perspective.